Question: Simplify to lowest terms. $\dfrac{120}{96}$
Solution: There are several ways to tackle this problem. What is the greatest common factor (GCD) of 120 and 96? $120 = 2\cdot2\cdot2\cdot3\cdot5$ $96 = 2\cdot2\cdot2\cdot2\cdot2\cdot3$ $\mbox{GCD}(120, 96) = 2\cdot2\cdot2\cdot3 = 24$ $\dfrac{120}{96} = \dfrac{5 \cdot 24}{ 4\cdot 24}$ $\hphantom{\dfrac{120}{96}} = \dfrac{5}{4} \cdot \dfrac{24}{24}$ $\hphantom{\dfrac{120}{96}} = \dfrac{5}{4} \cdot 1$ $\hphantom{\dfrac{120}{96}} = \dfrac{5}{4}$ You can also solve this problem by repeatedly breaking the numerator and denominator into common factors. For example: $\dfrac{120}{96}= \dfrac{2\cdot60}{2\cdot48}= \dfrac{2\cdot 2\cdot30}{2\cdot 2\cdot24}= \dfrac{2\cdot 2\cdot 2\cdot15}{2\cdot 2\cdot 2\cdot12}= \dfrac{2\cdot 2\cdot 2\cdot 3\cdot5}{2\cdot 2\cdot 2\cdot 3\cdot4}= \dfrac{5}{4}$